gradient_descent.ipynb

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    "This function creates the gradient component for each Theta value. The gradient is the partial derivative by Theta of the current value of theta, minus a \"learning speed factor alpha\" times the average of all the cost functions for that theta. For each Theta there is a cost function calculated for each member of the dataset."
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    "def Cost_Function_Derivative(X,Y,theta,j,m,alpha):\n",
    "    sumErrors = 0\n",
    "    for i in range(m):\n",
    "        xi = X[i]\n",
    "        xij = xi[j]\n",
    "        hi = Hypothesis(theta,X[i])\n",
    "        error = (hi - Y[i])*xij\n",
    "        sumErrors += error\n",
    "    m = len(Y)\n",
    "    constant = float(alpha)/float(m)\n",
    "    J = constant * sumErrors\n",
    "    return J"
   ]
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   "source": [
    "For each theta, the partial differential. The gradient, or vector from the current point in Theta-space (each theta value is its own dimension) to the more accurate point, is the vector with each dimensional component being the partial differential for each theta value"
   ]
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   "cell_type": "code",
   "execution_count": 13,
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   "source": [
    "def Gradient_Descent(X,Y,theta,m,alpha):\n",
    "    new_theta = []\n",
    "    constant = alpha/m\n",
    "    for j in range(len(theta)):\n",
    "        CFDerivative = Cost_Function_Derivative(X,Y,theta,j,m,alpha)\n",
    "        new_theta_value = theta[j] - CFDerivative\n",
    "        new_theta.append(new_theta_value)\n",
    "    return new_theta"
   ]
  }
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